4/3j + 5/6k = 13 -1/j +5/k = -3

Question

Solve the system:

4/3j + 5/6k = 13

-1/j + 5/k = -3

Answer 1

I read this as 4/(3j)+5/(6k)=13, -1/j+5/k=-3.

Let a=1/j and b=1/k then:

(4/3)a+(5/6)b=13, -a+5b=-3, so a=5b+3.

Substitute for a in the other equation:

(4/3)(5b+3)+(5/6)b=13, that is:

8(5b+3)+5b=78,

40b+24+5b=78,

45b=54, b=54/45=6/5, so k=⅚.

a=5b+3=6+3=9, so j=1/9.

CHECK:

(4/3)9+(5/6)(6/5)=12+1=13 OK;

-9+6=-3 OK.

So solution is (j,k)=(1/9,⅚).